find the surface area of a right prism with the given features: The bases are trapezoids with bases of lengths 6 and 10 perpendicular to one side of the length 12 ; height = 12

Round the answer to the nearest square unit

The prism has six sides. The two trapezoidal bases have areas of 8*12 = 96, each

The four rectangular sides have areas
12*6, 12*10, 12*12 and 12*sqrt(160)
I used the Pythagorean theorem for the last one.
Add up the areas.

Why did the right prism go to the doctor? Because it had a case of "base" fever! Let's help this prism feel better and find its surface area, shall we?

To find the surface area, we need to calculate the areas of all the sides and then add them up.

First, let's find the area of one trapezoid base. The formula for the area of a trapezoid is (a + b) / 2 * h, where a and b are the lengths of the bases and h is the height.

For the first trapezoid:
a = 6, b = 10, and h = 12.

Area of the first trapezoid = (6 + 10) / 2 * 12 = 96 square units.

Now, let's find the area of the second trapezoid, which is the other base. Since the length of the prism is 12 units, the bases are identical.

Area of the second trapezoid = 96 square units.

Next, we need to find the lateral areas, which are the rectangle-shaped sides of the prism. In a right prism, the lateral areas are always rectangles.

We have two lateral areas, and both are rectangles.
Length of the rectangle = 12 units (the height of the prism).
Width of the rectangle = the perimeter of the trapezoid base, which is the sum of all four sides.

For the first lateral area, the sum of all four sides is: 6 + 10 + 12 + 12 = 40 units.
Area of the first lateral area = length * width = 12 * 40 = 480 square units.

For the second lateral area, it will have the same area: 480 square units.

Now, let's add up all the areas to find the surface area:
Surface area = 96 + 96 + 480 + 480 = 1152 square units.

So, the surface area of the right prism is approximately 1152 square units!

To find the surface area of a right prism with trapezoidal bases, we need to calculate the area of the bases and the area of the lateral faces.

Step 1: Calculate the area of each trapezoidal base.

The formula to calculate the area of a trapezoid is: ((a + b) / 2) * h, where a and b are the lengths of the bases, and h is the height of the trapezoid.

Base 1:
Length of base = 6
Length of other base = 10
Height = 12

Area of Base 1 = ((6 + 10) / 2) * 12 = 96 square units

Base 2:
Length of base = 6
Length of other base = 10
Height = 12

Area of Base 2 = ((6 + 10) / 2) * 12 = 96 square units

Step 2: Calculate the area of the lateral faces.

The lateral faces of a right prism are rectangles with lengths equal to the perimeter of the base and a height equal to the height of the prism.

Perimeter of Base 1 = 6 + 10 + 6 + 10 = 32

Area of Lateral Face 1 = Perimeter of Base 1 * Height = 32 * 12 = 384 square units

Perimeter of Base 2 = 6 + 10 + 6 + 10 = 32

Area of Lateral Face 2 = Perimeter of Base 2 * Height = 32 * 12 = 384 square units

Step 3: Add up the areas of the bases and the lateral faces.

Total Surface Area = Area of Base 1 + Area of Base 2 + Area of Lateral Face 1 + Area of Lateral Face 2
Total Surface Area = 96 + 96 + 384 + 384
Total Surface Area = 960 square units

Therefore, the surface area of the right prism is 960 square units.

To find the surface area of a right prism with trapezoidal bases, we need to calculate the area of the bases and the lateral surface area.

Step 1: Calculate the area of the bases.
The bases are trapezoids with bases of lengths 6 and 10 and a height of 12. To find the area of a trapezoid, use the formula:

Area = (a + b) * h / 2

where a and b are the lengths of the bases, and h is the height.

For the first base:
Area1 = (6 + 10) * 12 / 2 = 96 square units

For the second base:
Area2 = (6 + 10) * 12 / 2 = 96 square units

Step 2: Calculate the lateral surface area.
The lateral surface area of a right prism is the sum of the areas of all its lateral faces. Since a right prism has rectangular lateral faces, we need to find the perimeter of the bases and multiply it by the height.

To find the perimeter of a trapezoid, add all the side lengths:

Perimeter = a + b + c + d

where a, b, c, and d are the sides of the trapezoid.

For the first base:
Perimeter1 = 6 + 10 + 12 + 12 = 40 units

For the second base:
Perimeter2 = 6 + 10 + 12 + 12 = 40 units

Now, multiply the sum of the perimeters by the height:

Lateral Surface Area = (Perimeter1 + Perimeter2) * height
Lateral Surface Area = (40 + 40) * 12 = 960 square units

Step 3: Calculate the total surface area.
To find the total surface area, we need to add the areas of the bases and the lateral surface area:

Total Surface Area = Area1 + Area2 + Lateral Surface Area
Total Surface Area = 96 + 96 + 960 = 1152 square units

Rounded to the nearest square unit, the surface area of the right prism is 1152 square units.